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5) Assuming £1.00 = $1.45 and €1.00 = $1.25, the interest rate in the UK is...

5) Assuming £1.00 = $1.45 and €1.00 = $1.25, the interest rate in the UK is 6.50% and the interest rate in Germany is 5.45%, determine the forward rate of the   £ / € if interest rate parity (IRP) holds. What does this imply about future forward rates? Explain how you can engage in covered interest arbitrage if the spot rate remains the same, and the interest rate in the UK is still 6.50%, and the forward rate is .868 £ / € .

Solutions

Expert Solution

£1.00 = $1.45 Therefore, £/$ = 1.00/1.45 = 0.6897

€1.00 = $1.25 Therefore, €/$ = 1.00/1.25 = 0.8

From above, £/€ = £/$ × $/€ = 0.6897 ÷ €/$ = 0.6897 ÷ 0.8 = 0.8621

As per Interest Rate Parity theory,

(Assumed 1 year forward rate)

Forward Rate of £/€ = Spot £/€ × [(1+ Interest Rate in UK)/(1+ Interest Rate in Germany)]

= 0.8621 × [(1+0.065)/(1+0.0545)] = 0.8707

Interest Rate Parity implies that the difference between the exchange rates (future rate and spot rate) will be equivalent to the difference between the interest rate of both countries. In other words, difference between the interest earned on both countries' interest rates will be equivalent to the Forward Premium/Discount.

In given case, if equal amount is invested in UK and Germany, i.e. £0.8621 in UK and €1 in Germany, then that would yield £0.9181 (0.8621+6.5% interest) and €1.0545 (1+5.45% interest), that would imply exchange rate after 1 year would be £/€ = £0.9181/€1.0545 = 0.8707(approx).

Opportunity for Covered Interest Arbitrage exists, where Forward Rate as per Interest Rate Parity is different from actual i.e. prevailing forward rate

In given case, Forward Rate as per IRP is 0.8707 and actual is 0.868

Therefore, Actual Rate < Theoretical Rate. So, Actual Rate is undervalued. Arbitrage Gain can be made by Buying Forward and Selling Spot.

Steps for Arbitrage:

Now,

(1) Borrow €10000 for 1 year @5.45%

(2) Convert €10000 into £ at spot rate i.e. £/€ = 0.8621 and receive £8621

(3) Invest £8621 @6.5 for 1 year

(4) Enter into 1 year forward contract to sell £9181.36 (proceeds of investment that will be received after 1 year) at £/€ = 0.868

After 1 year,

(5) Receive the proceeds of investment i.e. £9181.36

(6) Convert £9181.36 into € under the forward contrat that was entered and receive €10577.6 (£9181.36 ÷ 0.868)

(7) Reapy the borrowed € alongwith interest i.e. €10545 (€10000 + 5.45%)

Arbitrage Gain = €10577.6 - €10545 = €32.6

jeff jeffy answered 6 months ago
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